⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡵⡅⠋⢳⣹⣆⠁⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢶⠖⠂⠀⡤⠀⠀⠀⠀⠀⠀⠀
⣝⢦⡈⠲⢤⣀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠁⢻⡾⣵⣦⣾⡏⡿⡀⠁⠀⠀⠀⠀⠀⠒⠙⠒⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⣴⣵⠷⠊⠉⠀⠀⠀⠀⠡
⠀⠙⠺⠷⣀⣀⠴⠂⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⢾⢿⣿⢶⣶⢆⡈⠻⠿⣧⡻⣆⡠⠀⠀⠀⠀⠀⠀⣨⡵⣾⣱⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⡥⡄⠀⣠⢸⠀⠀⠀⠀
⠄⠀⠀⠀ ⠤⢴⣖⣛⣛⣭⡄⡇⠐⢁⠣⠀⠀⠀⠒
⣠⠴⠚⠁⠀⠀⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣻⣂⣀⠀⠀⣻⡄⠀⠀⠀⢻⣷⡀⢸⡧⢠⣿⠟⠃⠁⣠⣴⣾⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⡇⠀⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠓⠛⠋⠉⠋⠙⠋⠀⠃⠀⠀⠀⠀⡏⢷⢺⡇⠘⡿⠀⢀⡞⢡⣾⣿⡟⠋⠁⣴⣮ ⣹⣿⣿⣿⣿⡿⢡⡿⣄⡷⠂⠀⠀⠀⠀
⠠⠀⠀⠀⢀⣾⡕⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢶⣶⣲⣲⡶⠶⢤⣄⡀⠀⠀⢀⡇⣿⣼⣷⣤⣷⣀⡼⣸⣿⣿⡟⠀⠀⠰⣿⣿ ⣿⣿⣿⣿⣿⢁⡜⠀⢹⠁⡎⡞⠀⠀⣴
⡁⠀⠀⠀⣵⣯⠴⠶⢿⠀⠀⢀⣀⣤⢴⣖⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢦⣤⣿⣾⠿⡟⣏⠻⣿⣿⣇⣿⠛⠻ ⠷⠶⠶⠾⣿⢿ ⢿⡿⠿⣋⣡⠞⠁⠀⢸⣿⢰⠁⣀⡀⠀
⠈⠁⢂⠶⠃⠀⠀⣤⠾⣛⣛⣡⣴⣾⣿⣿⣿⠟⠋⠀⢸⣿⣙⢿⣿⣿⣿⣿⣿⣿⠿⣝⣿⠷⣄⢿⣾⠰⠿⠟⢿⣛ ⡿⠛⠙⠛⢿⠟⢟⡿ ⠛⠛⠛⠋⠀⠀⠀⠀⠈⣇⡋⡸⢀⠹⡄
⣂⡈⠀⠀⠀⠀⠀⢘⣦⣌⠻⣿⣿⣿⣿⡿⠁⠀⠀⠰⣿⣿⣿⣿⣿⣿⡟⣿⣵⣾⡿⠏⠉⠓⠀⢸⣿⡇⠀⠀⠀⠉⠓⠀⠀⠀⠀⡠⡺⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠃⠟⢧⢻
⣿⣤⣤⣄⠀⠀⢀⡼⠀⡟⢧⣈⠻⣿⡟⠀⠀⠀⠀⢸⣿⣿⡿⢟⣫⣷⡿⣻⣽⣿⠁⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢰⠀⠘⠸
⠈⠙⠲⠤⣀⣀⣾⠟⠀⡇⠀⠙⣷⣌⣙⠳⠶⠶⠶⢚⣻⣵⢾⡿⠏⠁⠈⢡⡿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀
⢦⡀⠀⠀⣤⣿⣁⣀⡀⣧⠀⠀⠈⠻⣿⣿⣟⡻⢋⢙⡫⠚⠁⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⢠⠘⢃⠀
⢀⣹⠦⠾⠯⠤⣴⣖⣂⣿⠀⠀⠀⠀⠀⠀⠙⠓⢷⣫⡄⠀⠀⠀⡠⠒⠅⢻⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⢰
⣏⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡤⠀⡠⢀⠀⠘⡿⣶⣶⣦⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠁⠀⡞
⠉⠻⣽⡶⣤⡿⠉⡷⣦⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠊⢀⢔⡴⠋⠀⣪⣾⠟⠗⠉⠃⢀⣠⣤⣠⣤⣶⠶⣦⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠁⣸⢀
⠻⣦⣀⣉⣷⣷⠈⡟⢦⣹⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢖⠁⠀⠀⢈⢾⡿⠁⠀⢀⣴⣶⣿⡿⠿⠿⠖⠛⠛⠚⠷⠶⣯⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠶⠾⣿⠋
⠀⠈⠻⢿⡷⣼⡄⢹⡠⣝⢯⡳⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣡⡾⢋⣜⡿⠋⠀⣠⣖⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣧ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢒⠄⢠⢀
⠀⠀⠀⠈⠹⣿⣧⡀⠁⢈⣙⣻⡝⢷⡀⠀⢀⠀⠀⠀⢠⣟⣾⠟⠱⠋⠈⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⡀⠀⠀⠀⠀⠀⠀ ⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⣄⣷⣿⣷⡁⠛
⠀⠀⠀⠀⠀⠈⢯⣷⣄⠘⢧⡉⢿⡌⣷⣤⢿⣆⠀⠐⣾⠿⡵⣠⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⣠⡴⣶⡿⢫⠟⠻⠛⠛⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⢹⢻⣿⣿⣏⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣝⢷⣄⠙⣦⡉⢩⡏⠀⢹⣆⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⣀⣤⠞⢁⢞⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⣾⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢹⣿⣦⣹⡟⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢐⠕⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣻⡿⣱⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⢹⣿⡟⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⢏⡿⣳⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢀⣠⣾⣟⣥⣾⡽⡿⠁⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢀⣀⣤⣤⣶⣾ ⣽⣿⣿⣿⡿⣻⣟⣾⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡽⣻⣶⣶⣦⣄⣀⠀⠀⠀⠀⢀⣀⣤⣶⣶⢿⣿⣿⣿⣿⣷⣶⢿⣿⣿ ⣿⣿⣿⣟⣵⣿⢯⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢿⣿⣯⣴⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣻⣟⢄⣾⢿⣏ ⡟⣽⢟⡾⣵⣳⣷⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣯⣟⣟⣿⢿⣋⣽⢋⣿⣿⡿⣱⣿⢏⣾⣯⢯⣾ ⣿⡽⢛⣿⣿⢏⠘⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣫⣾⡟⠘⣵⣿⣯⣿⣿⣿⣿⣟ ⣿⣿⣿⢯⢯⢿⣇⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⢆⠀⠀⠀⠀⠀⢰⡧⠚⠉⠁⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⢀⣾⡷⣿⣿⣿⣿⣷⣯⢯ ⣾⠇⣟⠛⠛⠚⠚⠤⣬⣛⢦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠈⢳⡄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣞⣟⡿⢽⣷⣻⣿⢡⢯ ⣿⣦⣻⠀⠀⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⡿⣳⠀⠀ ⠙⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀ ⠀⢸⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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